In a typical multiple description coding arrangement, a given signal to be transmitted is processed in a transmitter to generate multiple descriptions of that signal, and the multiple descriptions are then transmitted over a network or other communication medium to a receiver. Each of the multiple descriptions may be viewed as corresponding to a different transmission channel subject to a different loss probability. The goal of multiple description coding is generally to provide a signal reconstruction quality at the receiver that improves as the number of received descriptions increases, without introducing excessive redundancy between the various multiple descriptions.
One known multiple description coding technique is commonly referred to as quantized frame expansion. The signal to be transmitted may be represented as an N-dimensional symbol vector x={x1, x2, . . . , xN}. The symbol vector x is multiplied by a frame expansion transform T to generate an M-dimensional symbol vector y=Tx={y1, y2, . . . , yM}, where the transform T is an M×N matrix and M>N. The symbol vector y is then subject to a quantization operation to form Y=Q(y). Forward error correction (FEC) and cyclic redundancy check (CRC) codes are then applied to Y before it is transmitted over a network to the receiver. At the receiver, the received signal {tilde over (Y)} is subject to FEC decoding and the CRC is used to detect symbol errors. The symbols with no errors are used to reconstruct an estimate of x. For additional details regarding this and other conventional multiple description coding techniques, see Vivek K Goyal, “Multiple Description Coding Compression Meets the Network,” IEEE Signal Processing Magazine, September 2001, pp. 74-93.
Conventional multiple description coding techniques generally assume that the channels are so-called “erasure” channels. With such channels, a given symbol or other piece of data is known to the receiver to be either correct or in error, and some mechanism is needed to provide this capability, such as the above-noted FEC or CRC codes. However, the FEC or CRC codes are useful only for error detection and correction, and cannot otherwise be used to enhance the quality of a reconstructed signal when no errors occur. Use of such codes therefore represents a waste of bandwidth in any channels that do not have errors.
U.S. patent application Ser. No. 12/652,390, filed Jan. 5, 2010 and entitled “Orthogonal Multiple Description Coding,” discloses improved multiple description coding techniques that overcome the above-described drawbacks of conventional multiple description coding. In one such technique, multiple descriptions of a given signal are generated by processing the signal using respective ones of a plurality of orthogonal matrices. Each of the multiple descriptions is generated as a function of the signal and a corresponding one of the plurality of orthogonal matrices. For example, M descriptions y(i) of an N-dimensional symbol vector x may be generated by applying respective ones of the orthogonal matrices to the vector x in accordance with the following equation:y(i)=U(i)x, i=1, . . . , M. where U(i), i=1, 2, . . . , M denote orthogonal matrices of dimension N×N. The orthogonal matrices introduce redundancy in such a way that the redundancy can be used not only to improve signal reconstruction quality, but also to detect and correct errors in the received signal. The multiple descriptions therefore have error detection and correction capability built into them. This avoids the need to dedicate additional bandwidth for FEC and CRC, thereby ensuring that there will be no wasted bandwidth in the absence of errors, while also providing graceful degradation in the presence of errors.
Despite the considerable advantages provided by the above-described orthogonal multiple description coding technique, a need remains for further improvements, particularly with regard to providing optimal coding in the presence of variable channel conditions. For example, in coding techniques in which multiple description coefficients are subject to quantization prior to transmission, the bit rate and signal quality is fixed by the quantization level regardless of the actual channel condition. As a result, the bit rate and signal quality may be too low for a good channel, and may be too high for a poor channel. Therefore, such transmissions can lead to either a waste of bandwidth for good channels, or a failure to receive the signal in poor channels. Furthermore, in some systems, the number of transmission subcarriers is required to match the number of coefficients to be transmitted, which unduly limits the applications in which such systems can be used.